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Statistical inference of entropy functions of generalized inverse exponential model under progressive type-II censoring test

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  • Qin Gong
  • Bin Yin

Abstract

This article explores the estimation of Shannon entropy and Rényi entropy based on the generalized inverse exponential distribution under the condition of stepwise Type II truncated samples. Firstly, we analyze the maximum likelihood estimation and interval estimation of Shannon entropy and Rényi entropy for the generalized inverse exponential distribution. In this process, we use the bootstrap method to construct confidence intervals for Shannon entropy and Rényi entropy. Next, we select the gamma distribution as the prior distribution and apply the Lindley approximation algorithm to calculate `estimates of Shannon entropy and Rényi entropy under different loss functions including Linex loss function, entropy loss function, and DeGroot loss function respectively. Afterwards, simulation is used to calculate estimates and corresponding mean square errors of Shannon entropy and Rényi entropy in GIED model. The research results show that under DeGroot loss function, estimation accuracy of Shannon entropy and Rényi entropy for generalized inverse exponential distribution is relatively high, overall Bayesian estimation performs better than maximum likelihood estimation. Finally, we demonstrate effectiveness of our estimation method in practical applications using a set of real data.

Suggested Citation

  • Qin Gong & Bin Yin, 2024. "Statistical inference of entropy functions of generalized inverse exponential model under progressive type-II censoring test," PLOS ONE, Public Library of Science, vol. 19(9), pages 1-29, September.
    • Handle: RePEc:plo:pone00:0311129
    DOI: 10.1371/journal.pone.0311129
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    References listed on IDEAS

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    1. Alexandre Berred & Alexei Stepanov, 2022. "Asymptotic properties of lower exponential spacings under Type-II progressive censoring," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(14), pages 4841-4853, July.
    2. Zhang, Chunfang & Wang, Liang & Bai, Xuchao & Huang, Jianan, 2022. "Bayesian reliability analysis for copula based step-stress partially accelerated dependent competing risks model," Reliability Engineering and System Safety, Elsevier, vol. 227(C).
    3. Nguyen Ngoc Thach, 2023. "Applying Monte Carlo Simulations to a Small Data Analysis of a Case of Economic Growth in COVID-19 Times," SAGE Open, , vol. 13(2), pages 21582440231, June.
    4. Hanlin Li & Longxia Qian & Jianhong Yang & Suzhen Dang & Mei Hong, 2023. "Parameter Estimation for Univariate Hydrological Distribution Using Improved Bootstrap with Small Samples," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 37(3), pages 1055-1082, February.
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